In this paper, the aperture averaged scintillations of the Bessel beams carrying optical vortices propagating in turbulent atmosphere are evaluated. The multistep form of the propagation algorithm and a numerical phase screen simulation method are applied to the calculations of the aperture averaged scintillation. The results show that the Bessel beam with more topological charges delivers the smaller scintillation. The relation between the aperture averaged scintillation and the size of the beams is investigated. The effect of inner and outer scales of turbulence on the scintillations of the Bessel beams is also studied. These results may be useful in long-distance optical communications in free space or in turbulent atmosphere.